These are normal.
This one merely means that certain classes are not directly assigned in the the theme css. Fortunately, Nemo (and Nemo is unusual in this), will use its own Nautilus code to grab the properties outlined in the css file anyway.
You can manually change desktop handlers using dconf-editor:
sudo apt install dconf-editor
Then navigate the path it shows - /org/nemo/desktop/ignored-desktop-handlers and set the settings as you wish.
The reason for the 'error' is that Gnome-Shell is installed and running.
It's handling things, though, and is not a big deal. Again, this just falls to user preference, especially if you use Desktop Icons (I don't. I like my desktop completely clean and uncluttered, myself).


The Lightdm-gtk-greeter-settings GUI app has a lot of options, but is really only the tip of the iceberg of what you can do.